Duchamp, Gérard H. E.; Luque, Jean-Gabriel; Penson, Karol A.; Tollu, Christophe Free quasi-symmetric functions, product actions and quantum field theory of partitions. (English) Zbl 1187.05079 Sémin. Lothar. Comb. 54A, B54Am, 12 p. (2005). Summary: We investigate two associative products over the ring of symmetric functions related to the intransitive and Cartesian products of permutation groups. As an application, we give an enumeration of some Feynman type diagrams arising in Bender’s QFT (quantum field theory) of partitions. We end by exploring possibilities to construct noncommutative analogues. MSC: 05E05 Symmetric functions and generalizations 11P81 Elementary theory of partitions 81T18 Feynman diagrams Keywords:associative products; ring of symmetric functions; Cartesian p[roducts; permutation groups; enumeration; Feynman type diagrams PDFBibTeX XMLCite \textit{G. H. E. Duchamp} et al., Sémin. Lothar. Comb. 54A, B54Am, 12 p. (2005; Zbl 1187.05079) Full Text: EuDML EMIS